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/*
Copyright (C) 2002 Ferdinando Ametrano
Copyright (C) 2000, 2001, 2002 RiskMap srl
This file is part of QuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://quantlib.org/
QuantLib is free software: you can redistribute it and/or modify it under the
terms of the QuantLib license. You should have received a copy of the
license along with this program; if not, please email ferdinando@ametrano.net
The license is also available online at http://quantlib.org/html/license.html
This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the license for more details.
*/
/*! \file mixedscheme.hpp
\brief Mixed (explicit/implicit) scheme for finite difference methods
\fullpath
ql/FiniteDifferences/%mixedscheme.hpp
*/
// $Id: mixedscheme.hpp,v 1.2 2002/02/26 12:15:54 nando Exp $
#ifndef quantlib_mixed_scheme_h
#define quantlib_mixed_scheme_h
#include <ql/FiniteDifferences/finitedifferencemodel.hpp>
namespace QuantLib {
namespace FiniteDifferences {
//! Mixed (explicit/implicit) scheme for finite difference methods
/*! See sect. \ref findiff for details on the method.
In this implementation, the passed operator must be derived
from either TimeConstantOperator or TimeDependentOperator.
Also, it must implement at least the following interface:
\code
typedef ... arrayType;
// copy constructor/assignment
// (these will be provided by the compiler if none is defined)
Operator(const Operator&);
Operator& operator=(const Operator&);
// inspectors
size_t size();
// modifiers
void setTime(Time t);
// operator interface
arrayType applyTo(const arrayType&);
arrayType solveFor(const arrayType&);
static Operator identity(size_t size);
// operator algebra
Operator operator*(double, const Operator&);
Operator operator+(const Operator&, const Operator&);
Operator operator+(const Operator&, const Operator&);
\endcode
\warning The differential operator must be linear for
this evolver to work.
\todo add Douglas Scheme
*/
template <class Operator>
class MixedScheme {
friend class FiniteDifferenceModel<MixedScheme<Operator> >;
protected:
// typedefs
typedef typename Operator::arrayType arrayType;
typedef Operator operatorType;
// constructors
MixedScheme(const Operator& L, double theta)
: L_(L), I_(Operator::identity(L.size())), dt_(0.0), theta_(theta) {}
void step(arrayType& a, Time t);
void setStep(Time dt) {
dt_ = dt;
if (theta_!=1.0) // there is an explicit part
explicitPart_ = I_-((1.0-theta_) * dt_)*L_;
if (theta_!=0.0) // there is an implicit part
implicitPart_ = I_+( theta_ * dt_)*L_;
}
Operator L_;
Operator I_;
Operator explicitPart_, implicitPart_;
Time dt_;
double theta_;
};
// inline definitions
template <class Operator>
inline void MixedScheme<Operator>::step(arrayType& a, Time t) {
if (theta_!=1.0) { // there is an explicit part
if (L_.isTimeDependent()) {
L_.setTime(t);
explicitPart_ = I_-((1.0-theta_) * dt_)*L_;
}
a = explicitPart_.applyTo(a);
}
if (theta_!=0.0) { // there is an implicit part
if (L_.isTimeDependent()) {
L_.setTime(t-dt_);
implicitPart_ = I_+( theta_ * dt_)*L_;
}
a = implicitPart_.solveFor(a);
// a = implicitPart_.SOR(a, 1e-8);
}
}
}
}
#endif
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